# A spheres-based support vector machine for pattern classification

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## Abstract

This paper proposes a new spheres-based support vector machine (SSVM) for binary data classification. The proposed SSVM is formulated by clustering the training points according to the similarity between classes, i.e., it constructs two spheres simultaneously by solving a single optimization programming problem, in which each point is as far as possible away from the sphere center of opposite class and its projection value on the directed line segment between the two centers is as far as possible not larger than the corresponding radius. This SSVM has a perfect geometric interpretation for its dual problem. By considering the characteristics of the dual optimization problem of SSVM, an efficient learning algorithm for SSVM, which can be easily extended to other SVM-type classifiers, based on the gradient descent and the clipping strategy is further presented. Computational results on several synthetic as well as benchmark datasets indicate the significant advantages of the SSVM classifier in the computational cost and test accuracy.

## Keywords

Support vector machine Spheres Projection Geometric interpretation Learning algorithm## Notes

### Compliance with Ethical Standards

### Conflict of interests

We declare that we have no any conflict with other people or organizations that can inappropriately influence our work.

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